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NAVAL

POSTGRADUATE

SCHOOLMONTEREY, CALIFORNIA

THESIS

Approved for public release; distribution is unlimited

SENSOR MODEL REQUIREMENTS FOR TAWS/IRTSS

OPERATION

by

Rachel Hughes

September 2007

Advisors: Andreas Goroch

Kenneth Davidson


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4. TITLE AND SUBTITLE Sensor Model Requirements for TAWS/IRTSSOperation

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Naval Postgraduate SchoolMonterey, CA 93943-5000

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13. ABSTRACT (maximum 200 words)

Possible improvements to the minimum resolvable temperature difference (MRTD) entered into TAWS are considered. FLIR92 ismodified to include atmospheric turbulence that depends on height in the atmosphere. Resultant MRTDs are compared to the

operational FLIR92 MRTD predictions excluding atmospheric turbulence. The difference in the MRTD is only apparent in thehigher frequency regime and is less than 0.05% of the MRTD values for a typical test case. MRTD is calculated by FLIR92 andNVThermIP over desert and marine locations and the resultant MRTDs entered into TAWS to compare maximum detection range.NVThermIP yielded a larger maximum detection range by up to 1.5% over the desert and 2% over water.

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14. SUBJECT TERMS TAWS, FLIR92, NVThermIP, Atmospheric Turbulence, MRTD

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ABSTRACT

Possible improvements to the minimum resolvable temperature difference (MRTD)

entered into TAWS are considered. FLIR92 is modified to include atmospheric turbu-

lence that depends on height in the atmosphere. Resultant MRTDs are compared to

the operational FLIR92 MRTD predictions excluding atmospheric turbulence. The

difference in the MRTD is only apparent in the higher frequency regime and is less

than 0.05% of the MRTD values for a typical test case. MRTD is calculated by

FLIR92 and NVThermIP over desert and marine locations and the resultant MRTDs

entered into TAWS to compare maximum detection range. NVThermIP yielded a

larger maximum detection range by up to 1.5% over the desert and 2% over water.

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TABLE OF CONTENTS

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

A. MOTIVATION FOR COMPARISON . . . . . . . . . . . . . . . 1

1. Current Status of TAWS . . . . . . . . . . . . . . . . . . 1

2. Differences Between FLIR92 and NVThermIP . . . . . . 2

3. Advantages and Disadvantages of FLIR92 . . . . . . . . 4

4. Advantages and Disadvantages of NVThermIP . . . . . . 5

5. Phenomena Missing from FLIR92 and NVThermIP . . . 6

B. MOTIVATION TO TEST IMPORTANCE OF OPTICAL TUR-

BULENCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

C. PROJECT OVERVIEW . . . . . . . . . . . . . . . . . . . . . . 7

1. Comparison Parameters . . . . . . . . . . . . . . . . . . 7

2. Comparisons in TAWS . . . . . . . . . . . . . . . . . . . 8

II. THERMAL IMAGING SYSTEMS PERFORMANCE MODELS 9

A. FLIR92 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1. MTFs Included in FLIR92 . . . . . . . . . . . . . . . . . 9

2. Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3. System Noise . . . . . . . . . . . . . . . . . . . . . . . . 25

4. Calculating the Predicted MRTD . . . . . . . . . . . . . 30

5. Calculating the Predicted MDTD . . . . . . . . . . . . . 32

6. MRTD and MDTD Temperature Dependence . . . . . . 33

7. Johnson Criteria and FLIR92 . . . . . . . . . . . . . . . 33

B. NVTHERMIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1. MTFs Included in NVThermIP . . . . . . . . . . . . . . 34

2. Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3. System Noise . . . . . . . . . . . . . . . . . . . . . . . . 41

4. Calculating the Predicted MRTD . . . . . . . . . . . . . 43

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LIST OF TABLES

I. 3-D Noise Component Descriptions in FLIR92 . . . . . . . . . . . . . . 25

II. 3-D Noise Components For Scanning Systems . . . . . . . . . . . . . . 27

III. 3-D Noise Component For Staring Systems . . . . . . . . . . . . . . . . 27

IV. NVESD Recommended Settings for Psychophysical Constants . . . . . 31

V. Ezoom Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

VI. 3-D Noise Component Descriptions in NVThermIP . . . . . . . . . . . 41

VII. Noise Values for Scanning Systems in NVThermIP . . . . . . . . . . . 42

VIII. Noise Values for Staring Systems in NVThermIP . . . . . . . . . . . . 42

IX. Parameters for C2n Test Cases. . . . . . . . . . . . . . . . . . . . . . . . 53

X. Atmospheric Parameters around White Sands. . . . . . . . . . . . . . . 60

XI. Atmospheric Parameters around Point Conception. . . . . . . . . . . . 61

XII. Target Locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

XIII. Atmospheric Condition Variables for Input into Modified FLIR92. . . . 61

XIV. MRTD for Modified, Original FLIR92 in the horizontal direction. . . . 63

XV. MRTD for Modified, Original FLIR92 in the vertical direction. . . . . . 64

XVI. Input Parameters NVThermIP Part I. . . . . . . . . . . . . . . . . . . 95

XVII. Input Parameters NVThermIP Part II. . . . . . . . . . . . . . . . . . . 96

XVIII. Input Parameters NVThermIP Part III. . . . . . . . . . . . . . . . . . 97

XIX. Input Parameters for FLIR92 Part I. . . . . . . . . . . . . . . . . . . . 98

XX. Input Parameters for FLIR92 Part II. . . . . . . . . . . . . . . . . . . . 99

XXI. Acronyms Used in this Study . . . . . . . . . . . . . . . . . . . . . . . 101

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ACKNOWLEDGMENTS

Thanks to Jon Hixson at the Army Research Lab for informative teleconfer-

ences and helpful advice regarding NVThermIP. Thanks also to Prof Alf Cooper at

the Naval Postgraduate School for useful insights on sensor operations. Thanks to

the team at the Air Force Weather Agency (AFWA) for obtaining and interpreting

observational data on very short notice. Particular appreciation to my husband for

marshaling the AFWA team and for his thoughtful questions during late-night thesis

discussions.

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I. INTRODUCTION

Target Acquisition Weapons Software (TAWS) is used operationally to predict

the performance of electro-optical weapons and their navigation systems. For sensors

operating in the infrared (IR) spectral band, the minimum resolvable temperature dif-

ference (MRTD) is determined from a desktop computer model such as the Forward

Looking Infrared 92 (FLIR92) or the Night Vision Thermal and Image Processing

model (NVThermIP). Both models are capable of providing an MRTD, which may

be manipulated for use in TAWS, but there are differences in their calculations that

become apparent at high and low frequencies. Also, although FLIR92 does not oper-

ationally include the effects of atmospheric turbulence, NVThermIP does for limited

conditions.

In this study, FLIR92 and NVThermIP are compared in their current opera-

tional forms for various atmospheric conditions. Then FLIR92 is modified to include

atmospheric turbulence and the two version of FLIR92 are compared for the varied

atmospheric conditions.

All acronyms in this report are listed in alphabetical order in Appendix E.

A. MOTIVATION FOR COMPARISON

1. Current Status of TAWS

Currently, the MRTD used in TAWS predictions of target detection by IR

sensor is calculated by FLIR92 from basic system parameters. While this has been

sufficient for previous iterations of TAWS, recent improvements in model resolution

and the image resolution of sensors being modeled suggest that perhaps NVThermIP

may be a better choice. NVThermIP incorporates a number of improvements intended

to improve the determined MRTDs for the sensors in the extrema of low and high

spatial frequencies, in other words for very large and very small targets. NVThermIP

also includes optical turbulence, which should improve the MRTD calculation. With

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increased sensitivities of sensors, including optical turbulence should improve the

MRTD prediction. Since FLIR92 and NVThermIP behave differently at high and low

frequencies in marine or desert environments, one model may substantially improve

the MRTD calculation, and thus the TAWS predictions, over the other model. Inparticular, the temperature difference between the surface and the ambient air may

influence model calculations and this temperature difference is much greater during

the day over a desert.

2. Differences Between FLIR92 and NVThermIP

Both FLIR92 and NVThermIP are desktop computer models developed to

predict standard summary performance figures of merit for thermal imaging sys-

tems. They are PC based programs that model passive sensors which detect emitted

and reflected radiation. Using basic system-level parameters, these models calculate

the modulation transfer function (MTF), the noise equivalent temperature difference

(NETD), the MRTD, and the minimum detectable temperature difference (MDTD)

for sensors looking at specific targets. FLIR92 and NVThermIP both predict the

MRTD that a human can discriminate when using a thermal imager operationally.

NVThermIP also predicts the range at which target acquisition will be successful,

using the specified thermal imager. Thus, the output from each model is used to

determine whether or not a system will achieve the MTF, system noise, MRTD, and

MDTD that is required to effectively perform a given mission. For each mission, the

conditions necessary to meet the target acquisition and discrimination requirements

may vary.

FLIR92 and NVThermIP share certain basic assumptions. These assumptions

are stated in the NVThermIP Users Manual (NVESD 2001), and follow the steps of

modeling FLIR systems outlined in the Infrared and Electro-Optical (IREO) Hand-

book Vol.4 (1993). All MTFs are assumed to be separable, so the total system MTF

is calculated as the product of all sub-system MTFs. This approach reduces calcula-

tion complexities because the analysis is simplified to one dimension and cross-terms

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are eliminated. However, there is almost always some calculation error associated

with assuming separability. This error becomes significant in certain cases such as for

diamond-shaped detectors, but is neglected in all FLIR92 and NVThermIP calcula-

tions regardless of detector shape and type (NVESD 2001).An MTF describes the spatial frequency response of a system. It is the contrast

at a given spatial frequency compared to the contrast at a lower frequency. The total

system MTF is a product of all component MTFs. Each MTF may be calculated

as the Fourier transform of the point spread function (PSF) of the component, or

the response of the imaging component to a point of light. An imaging system

will experience some degradation of the image due to imperfections in the optics,

electronics, or even the observer eye and this degradation is what the MTF describes.

If some system component did not contribute to the degradation, then the MTF for

that component would be unity (Driggers 1999).

Both FLIR92 and NVThermIP assume all blurs to be symmetrical in order to

keep all MTFs real. The models assume that there exists a region of the field of view

(FOV) that is isoplanatic. Goodman (1968) explains that in an isoplanatic, or space-

invariant, linear imaging system the image of a point-source will change location,

but not functional form, as the point source moves. The approximately isoplanatic

region of the FOV is modeled in FLIR92 and NVThermIP by a linear shift-invariant

process and the MTF in that region is approximated by symmetrical blur. The blur

is the result of real world effects on the image and can be due to aberrations and

other manufacturing defects in the optical system. For a point source, the image

is called a blur circle because diffraction, aberrations, manufacturing defects, and

assembly tolerances prevent perfect resolution of the singularity (Driggers 1999). In

FLIR92, the blur MTF is geometric and is discussed in further detail in the next

chapter. The symmetrical blur approximation is not an accurate reflection of real

world systems, so the blur approximation for the optics is not completely correct.

Similarly, assuming symmetrical blurs does not accurately reflect the electronics used

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in the various sensor systems under consideration: a low pass filter would not result

in a time delay or phase shift using this assumption, for example (NVESD 2001).

NVThermIP provides some new capabilities beyond FLIR92. NVThermIP

provides target acquisition performance predictions for staring imagers, not just thefirst and second generation thermal scanning sensors. In the NVThermIP calculation,

the MTF representing the function of the human eye includes factors that are ignored

in FLIR92. The MRTD prediction is changed from FLIR92; NVThermIP produces

contrast transfer functions (CTFs) as the primary output. A laboratory MRTD is cal-

culated, but is not comparable to the MRTD output from FLIR92. Also, NVThermIP

now uses the Targeting Task Performance (TTP) metric to predict the probability

of target detection, recognition, and identification at given ranges. FLIR92 uses the

Johnson criteria, but does not predict probabilities of detection, recognition, or iden-

tification (NVESD 2001). In this report, the TTP capabilities in NVThermIP are

neglected since only the MRTD results from FLIR92 are compared to those from

NVThermIP.

3. Advantages and Disadvantages of FLIR92

a. Advantages of FLIR92

Since NVThermIP uses the same basic MRTD prediction theory with

modifications to improve on FLIR92 (NVESD 2001), familiarity would be the primary

benefit of continuing with FLIR92. These modifications are discussed in the next

sections, regarding the advantages of NVThermIP. If FLIR92 operates at a sufficiently

accurate and precise level to satisfy the increasingly more stringent requirements in

operational use of TAWS, then there is no reason to change. Also, NVThermIP

does not calculate a MDTD, which is more useful for indicating thermal imager

performance for point sources and aperiodic targets. TAWS uses the MDTD for

certain calculations, when available. For these two reasons, if a simple modification

to FLIR92 to include optical turbulence improves the FLIR92 MRTD prediction, then

it would be advantageous to continue using FLIR92.

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b. Disadvantages of FLIR92

There are two major characteristics of FLIR92 that may lead to errors

in performance predictions for staring arrays in sensors being modeled. Improved

sensitivities in staring arrays mean that the limitations of the eye in detecting con-trasts is now restricting the performance of these sensors (NVESD 2001), but FLIR92

MRTD calculations do not include any adjustments due to less-than-perfect contrast

perceptions of the eye. Likewise, limitations on detector size, spacing, and fill factor

(ratio of active cell area to total array area (Driggers 1999)) can cause under-sampled

imagery for staring sensors. To avoid the under-sampled imagery, FLIR92 has an

absolute cutoff at the half sample rates of imagers (Nyquist frequency), but when

used with the Johnson criteria, it can lead to incorrectly negative predictions for

most staring imagers (NVESD 2001). FLIR92 also does not account for atmospheric

turbulence, which may be particularly significant in the highly turbulent regime just

above a hot noon-time desert.

4. Advantages and Disadvantages of NVThermIP

a. Advantages of NVThermIP

NVThermIP is considered an advance over FLIR92 primarily because it

addresses the two possible errors in FLIR92 performance predictions regarding staring

arrays, as discussed above. NVThermIP also does include atmospheric turbulence in

a fairly rudimentary form.

b. Disadvantages of NVThermIP

There are three major hesitations in switching to use NVThermIP with

TAWS. First is a lack of familiarity. Otherwise, since NVThermIP was developed to

address weaknesses in FLIR92, it should be advantageous to use. For instance, NV-

ThermIP uses the Targeted Task Performance (TTP) Metric instead of the Johnson

Metric to provide a better performance estimate. This result is then used, like with

FLIR92, to predict the target acquisition range performance for given sensors. Sec-

ond, while NVThermIP predicts the MRTD, it is a laboratory MRTD that is not

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comparable to the MRTD from FLIR92. Instead, NVThermIP predicts the CTF

(NVESD 2001), which must be manipulated before insertion into TAWS. Finally,

NVTHermIP does not produce an MDTD, but TAWS uses the MDTD for certain

applications.

5. Phenomena Missing from FLIR92 and NVThermIP

Despite improvements in NVThermIP, there are details missing from both

FLIR92 and NVThermIP. One important lack is the optical turbulence. NVThermIP

does include an average optical transmission input, but neither model considers the

effect of optical turbulence variations along the optical path from the target to the

sensor. The next section discusses this in more detail.

Neither FLIR92 nor NVThermIP have any adjustments for polarization of the

target. Since the system response varies depending on the polarization, this lack will

be especially apparent as imager sensitivities increase. Both models work best for

nearly symmetric targets, but may poorly represent more realistic cases.

B. MOTIVATION TO TEST IMPORTANCE OF OPTI-CAL TURBULENCE

Recently, sensors with higher resolution have been developed. These IR im-

agers are more sensitive to smaller targets, or a higher spatial frequency. In order

to effectively model the responses of these sensors, it is becoming necessary to con-

sider and perhaps include previously negligible effects like optical turbulence. At the

sensitivities of the new sensors, the range for minimum detectability may be signif-

icantly affected by slight variations in the optical turbulence along the path from

the target to the sensor, perhaps even as regards a vertical pathlength through the

atmosphere. Optical turbulence causes blurring around the edges of images (Fante

1980) and makes it more difficult to resolve the image of the target well enough to

identify it. According to the IREO Handbook Vol.3 (1993), the effects of pressure

variations due to atmospheric turbulence are typically negligible compared to those

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due to temperature and humidity fluctuations. In either very hot atmospheres such as

those that may be operationally important in South Asia, or in very sensitive appli-

cations - such as detection of a very small target, the effect of atmospheric turbulence

may become significant. Recent improvements in sensor responsivities have increasedthe number of operations in the sensitive applications category and therefore exam-

ining the potential impact of optical turbulence along the optical path through the

atmosphere is crucial.

C. PROJECT OVERVIEW

Two comparisons to test possible improvements to the MRTD calculation were

accomplished.First, a MatLab version of the operationally used FLIR92 was modified to in-

clude variations in optical turbulence along the pathlength. Then the original FLIR92

was compared to the modified FLIR92 to investigate the significance of improvements

in the MRTD. Resultant MRTDs were inserted into TAWS and the maximum detec-

tion ranges were compared. The generic IR sensor in TAWS was used and marine

and desert environments were tested.

Second, the MRTDs calculated by FLIR92 and by NVThermIP were com-

pared. All input parameters were held constant for each model. The resultant MRTDs

from FLIR92 and NVThermIP were entered into TAWS. The atmospheric conditions

were varied to test the marine and desert environments. In TAWS, the generic IR

sensor was used for all tests, modified to include the MRTD from either FLIR92 or

NVThermIP.

1. Comparison Parameters

To compare FLIR92 and NVThermIP under the conditions described, param-

eters calculated by each were compared. Factors to compare and evaluate in order to

determine the significance of any differences are the horizontal and vertical MRTDs

and system MTFs at specified spatial frequencies. Again, the extrema of frequencies

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are the regions of particular interest in this study. Because NVThermIP outputs the

CTF, in order to compare, the resultant CTF was multiplied by 2 times the scene

contrast temperature (SCT) to obtain the MRTD (Jon Hixson, personal communica-

tion).The terms horizontal and vertical directions as used in this report refer to

the along-bar and cross-bar directions of a four-bar target, as shown in Figure 1.

Horizontal TargetOrientation

h axis

v axis

7/2 fs

1/2 fs

Vertical TargetOrientation

h axis

v axis7/2 f

s

1/2 fs

Figure 1. Horizontal and Vertical Directions with Respect to a 4-Bar Target.

2. Comparisons in TAWS

Once the MRTDs were determined from FLIR92 and NVThermIP, the re-

sults were entered into TAWS. Then, the range output from TAWS was compared

for the various different iterations to determine how much and how significant the

improvements to the maximum detection range in TAWS were.

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MTFs are standard in FLIR92 and are summarized from the Analysts Reference

Guide (1993) and compared against original sources or the IREO Handbook (1993)

as specified. For scanning systems, the scan direction is assumed to be horizontal to

the bars of the target.a. Optical MTF

The optical MTF includes the diffraction-limited MTF and geometric

blur MTF. When available, the optical MTF may be replaced by a user-defined

version determined from direct measurements or ray tracing program predictions.

The diffraction-limited MTF describes the resolution limitations due to diffraction in

the optics of the sensor and is valid for a system with a circular, clear aperture ( IREO

Handbook Vol.4 1993). It it of the form

Hdl(fs) =2

arccos

fsD0

fs

D0

1

fsD0

2 (2.1)

where is the wavelength for diffraction in m and D0 is the optics aperture diameter

in mm. Since arccos(x) is only physical when 1 < x < 1, then the spatial frequencyfs, in cycles/mrad, must satisfy fs D0 . The diffraction limited MTF in the hori-

zontal direction is illustrated in Figure 2. For this report, the same inputs are usedin the horizontal and vertical directions, so the MTF in the vertical direction is the

same.

Apertures that are partially obscured or are not perfectly circular, or

aberrations in the optics may cause blurring of the image (Goodman 1968). The

optics MTF includes a geometric blur term to describe this phenomenon. If there is

no user input for the geometric blur MTF, then FLIR92 assumes the blur is Gaussian

and the MTF has the form

Hgb(fs) = exp(222f2s ). (2.2a)

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, in mrad, is the standard deviation for a circular Gaussian blur distribution. The

IREO Handbook Vol.4 (1993) clarifies: 2 is

2 =w2

8

(2.2b)

where w is the Gaussian blur spot diameter in mrad at the 1e

point.

Figure 3 shows the geometric blur MTF in the horizontal direction.

Again, with the inputs used in this report, the MTF is identical in the vertical direc-

tion.

b. Detector Spatial MTF

Also included in the prefilter MTF is the detector spatial MTF that

compensates for the finite size of the detector. FLIR92 assumes a rectangular detec-

tor geometry. Like for the optical MTF, the IREO Handbook Vol.5 emphasizes the

importance of a user-specified detector spatial MTF, particularly if the rectangular

detector geometry approximation is grossly inaccurate.

0 5 10 150.4

0.5

0.6

0.7

0.8

0.9

1Diffraction MTF H

Spat Freq (cy/mrad)

MTF

Figure 2. Diffraction Limited MTF in the Horizontal Direction.

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mation in most cases. The MatLab version of FLIR92 used in this analysis assumes

a non-SPRITE system and uses Equation 2.3b. Figure 4 shows the form of the de-

tector spatial MTF in the horizontal direction, and again it is identical in the vertical

direction.

0 5 10 150.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Det aprtr MTF H

Spat Freq (cy/mrad)

MTF

Figure 4. Detector Spatial MTF in the Horizontal Direction.

This plot is assuming a non-SPRITE scanning or staring system.

c. Focal Plane Array Integration MTF

For scanning systems, the prefilter MTF also includes a focal plane

array integration MTF introduced in the horizontal direction by the finite integration

time of the detector. If ti is the detector integration time in s and vs is the scan

velocity in mrad/s, the MTF has the form of diffraction, or

Hdi(fs) = sin(fsvsti)fsvsti

. (2.4)

This MTF is only significant for scanning systems because staring systems do not

require compensation for finite integration times since they do not move during de-

tection.

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d. Sample-scene Phase MTF

When considering sampled systems, the target location on the sampling

grid can cause a phase effect, or aliasing effect. The aliasing of high frequency noise

into the bandpass of the sampled signal can produce false signals or greatly increasednoise or interference (IREO Handbook Vol.3 1993). The MTF representing this phase

effect is

Hssp(fs) = cos

fsrN

z

. (2.5a)

Here, rN is the Nyquist frequency in cycles/mrad and z is the phase angle (rad) be-

tween the target under consideration and the detectors operating at rN. The Nyquist

frequency, or Nyquist limit, is the frequency at which no useful information is trans-

mitted and is taken as half the scene sample frequency. It is given as

rN =sz

2z(2.5b)

where sz is the number of samples per detector IFOV. Input frequencies above the

Nyquist limit are likely to appear as aliasing signals at the lower frequencies (IREO

Handbook). At optimal operation, z is set equal to 0, but for average conditions z

is set equal to 0.785 rad (45). In the inputs used for the MatLab version of FLIR92,

z is set to 0, or for optimal operation. This results in an MTF in the horizontal and

the vertical direction that is constant at unity for all frequencies since cos(0) is unity.

e. Image Motion MTF

Image motion MTFs are included in FLIR92 to account for how the

thermal system moves with respect to the scene being imaged. Two causes of these

movements may be linear motion of the sensor system or vibration of the sensor

platform. These movements are represented in the linear image motion MTF, random

image motion MTF, and sinusoidal image motion MTF.

The linear motion MTF explains smearing of the scene across the detec-

tors due to movement of the system platform. How significant the smear is depends

on how fast the platform is moving and how long the detectors are exposed to the

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where fehp is the electronics 3dB frequency in Hz. The low frequency response is only

significant at extremely low frequencies, so FLIR92 does not include it in the total

MTF, but Hehp is used to calculate noise bandwidths.

For the high frequency response, the low pass filter MTF is

Help(ft) =

1 +

ft

felp

2n1

2

(2.10b)

where like in the high pass filter case, felp is the 3dB frequency in Hz and n is the

number of filter poles. This high frequency response MTF is included in the total

MTF since the high frequency response is significant at a greater range of frequencies.

h. Boosting MTF

For the scanning system, an aperture correction MTF, or electronic

boosting MTF, is required. The boost emphasizes higher frequencies to compensate

for the reduced depth of modulation that typically occurs at higher frequencies due to

the less-than-ideal aperture response (IREO Handbook Vol.4 1993). It has the form

Heb(ft) = 1 +1

2(Ba 1)

1 cos

ftfb

. (2.11)

0 5 10 150.6

0.4

0.2

0

0.2

0.4

0.6

0.8

frequency (Hz)

J0

(fs

)

Zeroth Order Bessel Function

Figure 6. Zeroth Order Bessel Function

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fb is the frequency in Hz of the maximum boost and Ba is the amplitude of the boost

at a maximum frequency fmax. As the IREO Handbook Vol.4 observes, the boost

MTF is applied along the scan direction.

i. Electro-Optical Multiplexer MTFFor the LED electro-optical multiplexer, the MTF is of the form of

diffraction,

Heom(fs) =sin(fsLED)

fsLED(2.12)

and LED is the angular subtense of the LED element in mrad. Heom is not included

in the MatLab version of FLIR92.

j. Digital Filter MTF

Digital filters have a linear phase symmetrical impulse response which

varies depending on whether there is an even or an odd number of samples (N). For

N odd,

Hdf(fs)odd =(N1)/2

i=0

ai cos

2ifs

fco

. (2.13a)

For N even,

Hdf(fs)even =N/2i=1

ai cos

2

i 12

fs

fco

. (2.13b)

For these MTFs, ai is the digital filter coefficient and fco is the filter cut off frequency

in cycles/mrad. In the MatLab FLIR92, this MTF is set to unity for all frequencies

in both the horizontal and vertical directions.

k. Display MTF

Although many recent thermal imagers use a cathode ray tube (CRT)

display to communicate collected information to the observer, if a non-CRT display is

being used, FLIR92 requires a user-specified MTF. Otherwise, the model calculates

the total MTF based on a CRT display. In FLIR92, the phosphor spot luminance

intensity is assumed to have a Gaussian distribution with a value either specified

by the user or calculated by the model from the relationship

=

log(0.025)22f2Nr

(2.14)

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l. CCD Charge Transfer Efficiency MTF

For a CCD system, Sequin and Thompsett (1975) explained the charge

transfer efficiency MTF as due to the non-unity charge transfer efficiency of the

system. The CCD charge transfer efficiency MTF depends on the number of gatesin the transfer from the detector to the output amplifier (N) and the charge transfer

efficiency at each gate () along with the Nyquist frequency, or the sampling frequency

of the structure. As indicated in the IREO Handbook Vol.4, it may be expressed as

HCCD(fs) = exp

N(1 )

1 cos

2fs

rN

(2.17)

where rN is again the Nyquist frequency in cycles/mrad (see Section II.A.1.d). N

may be calculated in the model by assuming that the system has a interline transfer

scheme, but often is specified by the user. In the MatLab program being used, the

CCD Charge Transfer Efficiency MTF was set to unity for all frequencies, in both

the vertical and horizontal directions.

m. Display Sample and Hold MTF

Given that s is the sampling aperture in mrad, the display sample and

hold MTF has the form

Hdsh(fs) = sin(sfs)sfs. (2.18)

Figure 8 shows the horizontal display sample and hold MTF, but the vertical is set

in the MatLab code to be unity for all frequencies.

n. Eye MTF

The eye MTF encapsulates the influences of the observer. In FLIR92,

the eye MTF is based on work by Kornfeld and Lawson (1971). The observer may be

able to improve and optimize the system display by adjusting the gain and level, the

viewing distance, and the like. In this case, the eye MTF is considered non-limiting

and is considered a constant of unity since no degradation of the spatial frequency

response would be expected. In other words,

Heye(fs) = 1.0. (2.19a)

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The system noise filter MTF is not included in the total system MTF (HSY S) since

the component MTFs are already included in the total MTF, but will be referenced

in future sections. It may be expressed as

HNF(fs) = Hdi(fs)Hehp(fs)HTPF(fs)HSP F(fs) (2.20)

where for staring systems, HTPF(fs) is unity. The horizontal system noise MTF is

shown in Figure 10.

p. Total System MTF

The total system MTF is the product of all the component MTFs de-

scribed above. For the generic case described in this report, the total horizontal MTF

is shown in Figure 11. The downward curve of the MTF illustrates how much the

image is degraded, particularly at higher spatial frequencies, corresponding to small

targets.

0 5 10 15

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Display brt eye response

Spat Freq (cy/mrad)

MTF

Figure 9. Eye/Brain Response MTF.

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2. Sampling

a. Limits to Defined MRTD

In FLIR92, the MRTD is only defined for a periodic target such as a

4-bar target. The target must have a 7:1 aspect ratio, as shown in Figure 1 and thefour bars should be fully resolved by the observer in order to specify an MRTD. In

thermal imagers, the cutoff frequency for the observer to be able to fully resolve the

target s the systems Nyquist frequency. By definition, then, no MRTD can be given.

This limits FLIR92 to MRTD prediction below the Nyquist limit.

Since many targets are aperiodic, this artificial method of limiting the

MRTD prediction may be pessimistic. Information relating to the MRTD may be

available above the Nyquist limit, but methods for obtaining and quantifying thisinformation are not available for use in FLIR92.

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Horizontal Noise MTF

Spat Freq (cy/mrad)

MTF

Figure 10. Horizontal System Noise MTF.

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systems where the MRTD degradation is pronounced when there is a misalignment

between respective targets and detectors under consideration.

3. System Noise

FLIR92 characterizes second-generation thermal imaging systems and as such,

the system noise in MRTD predictions is modeled using a scaling factor that multiplies

the random spatio-temporal noise by the amount of excess system noise (Kennedy

1990). To simplify the model, the system noise is reduced to components that add in

quadrature. Appropriate eye spatial and temporal integration effects are considered

for each noise component included.

The Night Vision and Electronic Sensors Directorate (NVESD) of the US Army

in 1990 established a theoretical framework and a standard laboratory measurement

procedure to better characterize the noise in the system (Webb et.al. 1991). This

method of noise analysis isolates the system noise into eight components. These

components are listed in Table I along with possible sources of the noise.

Table I. 3-D Noise Component Descriptions in FLIR92Subscripts of noise components shown in table indicate dimension: t temporal, v

vertical spatial, h horizontal. Table derived from Analysts Reference Guide (1993).

Noise Description Potential Sourcetvh random spatio-temporal noise basic detector temporal noisetv temporal row noise line processing,

1f

, read-out

th temporal column noise scan effectsvh random spatial noise pixel processing, detector-to-detector

non-uniformityv fixed row noise detector-to-detector non-uniformity,

1f

h fixed column noise scan effects, detector-to-detector non-uniformity

t frame-to-frame noise frame processingS mean of all components

Here, tvh is the basic detector noise which is often characterized by the NETD

(see Equation 2.22, next section). The NETD is a sensitivity parameter. It is defined

as the temperature difference between the target and the background that will produce

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a peak signal to rms noise ratio of unity at the output of a reference filter. This is how

the NETD gives a rough estimate of how noisy a sensor is compared to the signals

being detected. All other components besides tvh must be added in quadrature

in order to completely characterize the thermal imaging systems noise (Scott et.al. 1993). In the current operational FLIR92, tvh is predicted but the remaining

components are measured or estimated. FLIR92 includes estimates of 3-D noise for

generic scanning and staring sensors so that when measurements are not available,

a calculation may still be made. More detailed descriptions of the system noise are

given in the sections following.

a. Defaults for 3-D Noise Components

In a given system where 3-D noise measurements have not yet beenmade or are not available, FLIR92 provides a set of default values. These default

values are only given for what FLIR92 considers significant noise components and

depend on the predicted random spatial-temporal noise, tvh. As discussed in Section

II.A.3, the system noise sources add in quadrature, so only the most significant noise

components are defaulted to non-zero components since the others would scarcely

affect the outcome of the noise calculation. These default values are from a database

of system noise measurements that were carried out by NVESD starting in April 1990.

The values for each system in the database are normalized to tvh and averaged with

other systems in the same class in order to determine which are the dominant noise

sources in that class and which are so small they may be neglected.

In scanning systems, the significant noise components are the temporal

row and the fixed row noises, tv and v. Scanning systems typically show a wide

range of variation in noise levels, so three default values are provided for both tv and

v. Table II shows the models default values for scanning systems.

In staring systems, the significant noise component is the random spa-

tial noise, vh. NVESD found a single default value for vh to be sufficiently repre-

sentative. This default value is shown in Table III.

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Table II. 3-D Noise Components For Scanning SystemsSubscripts of noise components shown in table indicate dimension: t temporal, vvertical spatial, h horizontal. Table derived from the Analysts Reference Guide

(1993).

Noise Term Low Noise Default Moderate Noise Default High Noise Defaulttv 0.25tvh 0.75tvh 1.0tvhv 0.25tvh 0.75tvh 1.0tvh

Table III. 3-D Noise Component For Staring SystemsSubscripts of noise components shown in table indicate dimension: t temporal, v ver-tical spatial, h horizontal. Table derived from the Analysts Reference Guide (1993).

Noise Term Noise Default

vh 0.40tvh

b. Random Spatio-temporal Noise, tvh

Since tvh is related to the actual bandwidth of the system, it may be

measured directly at the output port prior to display. However, as outlined in the

IREO Handbook Vol.4, it may otherwise be determined through the relationship to

the NETD,

tvh = NE TD

fpfN

(2.22)

where fN is the equivalent noise bandwidth for the NETD. In this case, fp isthe actual noise bandwidth which is associated with the system electronics before

display. In order to determine the equivalent noise bandwidth, given that S() is

the normalized detector noise power spectrum and Href() is the standard NETD

reference filter, the relationship used is

fN =

0

S()[Href()]2 d. (2.23)

The actual noise bandwidth differs depending on whether a scanning or staring system

is under consideration. When considering scanning systems, the noise bandwidth at

the system output port is of similar form to the equivalent noise bandwidth,

fp =

0

S()[HTPF()]2 d. (2.24)

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For staring systems, the actual noise bandwidth is given by

fp =

0

S()

sin(ti)

ti

2d (2.25)

and ti is the FPA integration time.

For all classes of systems, staring or scanning, the general form of the

random spatio-temporal noise is given in Equation 2.26,

tvh =4f2no

fp

0

Ad21

D(, 300) WT300

() d

. (2.26)

Here, fno is the optical f-number, fp is the system noise bandwidth as defined

in Equation 2.24 or 2.25, 0 is the optical transmittance, and Ad is the detector

area in cm2. The partial derivative is the thermal derivative of Plancks Law in

W/cm2/sr/m. The detector noise-limited spectral detectivity is D(, 300) in cm-

Hz1

2 /W and includes only noise components from the temporal noise sources since

the spatial noise source contributions are included in the system noise correction

functions described in the following section, II.A.3.c. Also, FLIR92 does not make

any adjustments for changes to detector responsivity due to cold shielding, so any

tweaking there must be off-line.

c. Noise Correction Functions

Since each 3-D noise component listed in Table I is assumed to be

statistically independent, the total system noise, filtered, may be written as the root

sum square of the noise components:

(fs) = 2tvhEtEvz(fs)Ehz(fs) +

2vhEvz (fs)Ehz(fs)

+ 2thEtEhz(fs) + 2tvEtEvz(fs) +

2vEvz(fs)

+ 2hEhz(fs). (2.27)

Here, Et, Ehz(fs) and Evz (fs) represent the eye or brain temporal and spatial integra-

tion associated with the noise components. The frame-to-frame term 2t Et has been

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dropped because the frame-to-frame noise t is almost always so small comparatively

that it is negligible. The orientation of the MRTD target under consideration is in-

dicated by the subscript z. In this case, the temporal integration may be expressed

in terms of FR, the system frame rate in Hz, E, the eye integration time in sec, andt, the temporal sample correlation length.

Et =t

FRE. (2.28)

In FLIR92, t is assumed to be unity in MRTD calculations. The spatial integra-

tions are simplified in the FLIR92 model and may be expressed in terms of sample

correlation factors h and v, horizontal and vertical sampling rates Rh and Rv in

samples/mrad, and spatial integration limits Lhz(fs) and Lvz(fs) in mrad

1

. Thesespatial integration limits are approximately the width and height of the MRTD bar

target. For staring systems, the samples in each direction are assumed independent

so that h and v are unity. For scanning systems, samples in the scan direction

may not be assumed independent due to the motion of the scanner, so h may be

greater than unity. Similarly, samples taken perpendicular to the scan direction may

be assumed independent since the motion of the scanner is cross-directional, so v

is unity. Although FLIR92 uses this simplified form, the exact expressions for thehorizontal and vertical eye/brain spatial integration are given in Appendix B.

In order to determine the noise terms for the horizontal and vertical

MRTD calculations, it is assumed that only noise components in the direction of the

MRTD target degrade the MRTD. For the MDTD, since target orientation does not

affect the calculation, the noise correction function is independent of direction. Given

the noise correction functions in the horizontal,

kh(fs) =1 + 2vh

2tvhE1t +

2th2tvh

[Evh(fs)]1 +

2h2tvh

[EtEvh(fs)]1 (2.29)

and in the vertical,

kv(fs) =

1 + 2vh2tvh

E1t +2tv

2tvh[Ehv(fs)]

1 +2v

2tvh[EtEhv(fs)]

1 (2.30)

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given in Table IV. Biberman (1973) showed using psychophysical data that SN RTH

is a function of the target spatial frequency, but the NVESD recommended value of

2.5 is a representative average for optimal observing conditions.

Table IV. NVESD Recommended Settings for Psychophysical ConstantsSettings in FLIR92 may be adjusted from NVESD recommendations.

Psychophysical Constant NVESD Recommended Setting Units

SN RTH 2.5 E 0.1 s

E depends on the background luminance. Luminances corresponding

to a 0.1 s eye integration time show agreement with display luminances that NVESD

measured in perception experiments in 1988. These experiments were conducted

under conditions similar to those used in MRTD measurements such as a darkened

room and optimal viewing. Observers set the display luminance to an average of

0.15 milli-Lamberts. Higher ambient light conditions typically correspond to greater

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (cy/mrad)

Temperature

Test horizontal and vertical MRT

Horizontal

Vertical

Figure 12. System MRTD showing the Horizontal and Vertical Results.The 2-D system MRTD is calculated by taking the geometric average of the

horizontal and vertical results, so it would lie between the two.

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display luminances and a faster integration time may be appropriate in these cases,

such as in the systems used in the field.

b. 2-D MRTD Calculation

FLIR92 can calculate a 2-D MRTD by taking the geometric mean ofthe horizontal and vertical MRTDs. In taking the geometric mean, each component

is weighted equally and the mean is with respect to the spatial frequency axis. This

causes the 2-D MRTD to asymptote at the mean value of the vertical and horizontal

cut-off spatial frequencies. These cut-off spatial frequencies are determined by either

the Nyquist limits or MTF roll off.

5. Calculating the Predicted MDTD

The basic form for the MDTD calculated in FLIR92 is

MDTD(fs) =SN RTHtvhkMDT(fs)

ATQh(fs)Qv(fs)

EtEh(fs)Ev(fs) (2.35)

where the MDTD is independent of target orientation, so kMDT(fs) is independent

of orientation and is given by Equation 2.33. Qh(fs), Qv(fs), and Ev(fs) are defined

below and are equivalent for both scanning and staring systems. Along the horizontal

direction, the eye/brain spatial integration differs for staring and scanning systems,

so each is stated below. AT is the target area in mrad2 and is related to the spatial

frequency, fs by

AT =

1

fs

2. (2.36)

Equation 2.36 assumes an isometric target, but is a poor approximation for many

operation targets that are not so uniform. All other variables are defined as for the

MRTD calculation.

The Qh(fs) and Qv(fs) integrals both include the total system MTF, HSY S.

If z represents the orientation, either horizontal or vertical, then the Qz(fs) integral

is

Qz(fs) =

[HSY Sz()]2

sin

fs

fs

2

d. (2.37)

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Table V. Ezoom ExamplesPortions of total FOV area shown on display screen when different Ezoom values areused. Values obtained from the NVThermIP Users Manual (2005).

Ezoom M Factor Vert FOV Seen Horiz FOV Seen Tot FOV Area Seen

none 1 1 1 1single 2 1/2 1/2 1/4double 4 1/4 1/4 1/16

where Sw is the physical width of the Gaussian display spot in cm and F OVz is the

FOV in either the horizontal (z = h) or the vertical (z = v) direction.

Also, unlike FLIR92, NVThermIP includes MTFs for other possible

display types besides CRT, but these are not discussed here since this report focuses

on comparing the two models using the same inputs.

l. CCD Charge Transfer Efficiency MTF

The CCD Charge Transfer Efficiency MTF is not included in NVThe-

rmIP, but could be entered by the user as one of the custom MTFs if so desired.

m. Display Sample and Hold MTF

The display sample and hold MTF of Equation 2.18 is again the same

in NVThermIP, but is only calculated for scanning systems. Also, it is only applied

when calculating the horizontal MTF.

n. Eye MTF

NVThermIP handles the eye MTF very differently from FLIR92. NV-

ThermIP considers the human eye point spread function as a combination of three

factors: the optics, the retina and the tremor. This leads to an MTF that may be

expressed as the product of the component MTFs from the eye optics Heo, the retina

Hret, and the tremor Htrem:

Heye(fs) = Heo(fs)Hret(fs)Htrem(fs). (2.44)

Overington (1976) outlines the theory of the human eye MTF and identifies the three

component MTFs above. Based on Overingtons work, the general forms for the eye

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MTF are found, but in In NVThermIP, these forms for the eye optical, retinal, and

tremor MTF are all empirical (NVESD 2001). The eye optics MTF is

Heo(fs) = exp 43.69

fsMsysfo

io

(2.45)

where Msys is the imaging system magnification, and fo and io are defined below,

fo = exp

3.663 0.0216D2p log10(Dp)

(2.46a)

io =

0.7155 + 0.277

Dp

2 . (2.46b)

The variable Dp is the pupil diameter in mm and is valid if one eye is used. If two

eyes are used, then NVThermIP reduces the pupil diameter by 0.5mm. Dp is defined

as

Dp = 9.011 + 13.23 exp log10(fL)

21.082

(2.46c)

where fL is the number of foot-Lamberts at the eye from the display and is fL =Ld

0.929.

Ld is the display luminance in milli-Lamberts. The retina MTF is defined as

Hret

(fs) = exp0.375

fs

Msys1.21

. (2.47)The tremor MTF, or the MTF of the eye due to tremor, is

Htrem(fs) = exp

0.4441

fs

Msys

2. (2.48)Clearly, then, the MTFs depend on the pupil diameter, which in turn depends on the

light level.

Figure 13 compares the eye MTFs in FLIR92 and NVThermIP. Clearly,NVThermIP has a more optimistic estimate of the image degradation due to the

observers eye, which reduces the known error in the FLIR92 modeling of the human

eye.

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o. System Noise Filter MTF

The system noise filter MTF is merely the roll-up of all the system

noise. In NVThermIP, there is a further factor for system noise that is requested as a

user-input. NVThermIP considers that each system has a different fixed pattern noiseassociated with variations in detector gain and level offset. There are three options

in the NVThermIP input: None, Noise Factor, and 3-D Noise. If None is selected,

then the system is considered ideal with no variations in gain and level offset among

the detectors. For Noise Factor, experimentally-determined independent horizontal

and vertical factors are multiplied by the horizontal and vertical noise CTFs. The

3-D Noise is discussed in a later section about system noise.

p. Interpolation MTF

NVThermIP includes an MTF for interpolation, or the process of in-

creasing the image size by inserting filler pixels between the original pixels. Interpo-

lation may be done either vertically or horizontally, and if interpolation is selected for

0 5 10 150.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Compare Eye MTF from FLIR92, NVThermIP

Spat Freq (cy/mrad)

MTF

FLIR92

NVThermIP

Figure 13. Comparing the Eye MTF in FLIR92 and NVThermIP in the HorizontalDirection.

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both directions, only one is applied at a time. The results are then combined. NV-

ThermIP offers three different methods for interpolation, Pixel Replication, Bilinear

Interpolation, and Bicubic Interpolation. In this report, since FLIR92 does not offer

interpolation, no interpolation is selected.q. Optical Turbulence MTF

Unlike FLIR92, operational NVThermIP already includes an MTF for

optical turbulence. This turbulence MTF assumes that C2n is constant along the

pathlength and so is an average MTF. C2n is a parameter that describes the optical

turbulence in the atmosphere and more thoroughly defined in Chapter III. The

formulation is very similar to the Goodman results for constant C2n given in Equation

A.98 in Appendix A. The equation is given below,

Hat(fs) = exp

57.4af53s C2n 13 z

1 1

2

fsD

13

(2.49)

where a is a constant defined as 38

, fs is here defined in cycles/rad, C2n is still in m

2

3 ,

and , z, and D are all in m.

2. Sampling

a. Sample Spacing

For an imaging system, the sample spacing quantifies the limits due to

sampling. For staring systems, the sample spacing can be calculated in the horizontal

and vertical directions by

SSz =F OVz

Nz(2.50a)

where z indicates the target orientation, either horizontal or vertical. Nz is the number

of detectors in the z direction. SSz is in mrad. For a scanning system, the vertical

sample spacing is calculated as per Equation 2.50a, but in the horizontal direction

the sample spacing is different. There is no sample spacing in a continuously scanning

system, so SSh = 0. A scanning system that samples has a sample spacing requires

a user-input of NHIFOV, or samples per HIFOV. Then the sample spacing is

SSh =DASh

NHIFOV. (2.50b)

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DASh is the detector angular subtense (DAS) in the horizontal direction, in other

words, the detector width divided by the focal length of the collecting optics.

b. Sample Frequency

As explained in Section II.A.2.b, the sampling frequency is just theinverse of the sample spacing, Equations 2.50a or 2.50b. Thus, the sampling frequency

is

fsamp =1

SSz. (2.51)

Since the horizontal and vertical sample spacing may differ, the horizontal and vertical

fsamp may also differ. Again the half sample frequency is the Nyquist frequency.

3. System Noise

As mentioned in Section II.B.1.o, the 3-D system noise is handled in a similar

manner to FLIR92. The 3-D system noise components are defined in Table VI,

essentially the same as Table I.

Table VI. 3-D Noise Component Descriptions in NVThermIPSubscripts of noise components shown in table indicate dimension: t temporal, v ver-tical spatial, h horizontal. Table derived from NVThermIP Users Manual (NVESD2005).

Noise Description Potential Source

tvh random spatio-temporal noise Basic Detector Temporal Noisetv temporal row noise, line bounce Line Processing,

1f

, read-out

th temporal column noise, columnbounce

Scan Effects

vh random spatial noise, bi-directional fixed pattern noise

Pixel Processing, Detector-to-DetectorNon-Uniformity 1

f

v fixed row noise, line-to-line non-uniformity

Detector-to-Detector Non-Uniformity

h fixed column noise, column-to-column non-uniformity

Scan Effects, Detector-to-DetectorNon-Uniformity

t frame-to-frame noise, framebounce

frame processing

S mean of all noise components

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As in FLIR92, these eight noise parameters are derived using directional av-

erages. tvh is predicted and all other components are estimated based on historical

databases of measurements. In Table VI, the subscript that is missing indicates which

directions were averaged so, for example, tv was averaged in the horizontal and v

in both the temporal and horizontal. Again similar to FLIR92, only certain noise pa-

rameters are considered important in scanning and staring systems. Table VII shows

the key parameters for scanning systems, where the noise term is normalized using

the random spatio-temporal noise tvh.

Table VII. Noise Values for Scanning Systems in NVThermIPSubscripts of noise components shown in table indicate dimension: t temporal, v ver-

tical spatial, h horizontal. Table derived from NVThermIP Users Manual (NVESD2005).

Noise Term Low Moderate High

vh/tvh 0 0 0v/tvh 0.25 0.75 1h/tvh 0 0 0

Table VIII shows the key parameters for staring systems, where the noise term

is again normalized with tvh. Table VIII compares to Table III.

Table VIII. Noise Values for Staring Systems in NVThermIPSubscripts of noise components shown in table indicate dimension: t temporal, v ver-tical spatial, h horizontal. Table derived from NVThermIP Users Manual (NVESD2005).

Noise Term Low Moderate High

vh/tvh 0.2 0.5 1 - 2v/tvh 0.2 0.5 1 - 2h/tvh 0.2 0.5 1 - 2

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a. Random Spatio-temporal Noise, tvh

The random spatio-temporal noise is calculated similarly in NVThe-

rmIP as in FLIR92, but includes a factor to account for the number of detectors.

Again, tvh is calculated assuming a background temperature of 300K and the rela-tionship,

tvh =4f2no

fp

0

AdN21

D(, 300) WT300

()d

(2.52)

where N is the number of detectors and all other variables are defined as for Equation

2.26. Note that Equation 2.52 differs from Equation 2.26 by a factor of in the

denominator.

4. Calculating the Predicted MRTD

NVThermIP outputs three laboratory measurements of the MRTD: high gain,

low gain, and user input. The basic equation used in all cases is

MRTDz(fs) =2SC NTMPCT Feye(fs)

(Abar(fs) Aspc(fs))SL

1 + 22detQHz(fs)QVz(fs)SC N2tmp

. (2.53)

Here, SC NTMP is the scene contrast temperature that generates the average display

luminance in K, CT Feye(fs) is the naked eye CTF, Abar is the area of the bar in thetarget in cm2, Aspc is the area of the space between bars in the target in cm

2, SL is

the unitless normalized laboratory detector responsivity, det is the noise variance in

K-mrad-s1

2 , and QHz and QVz are the horizontal and vertical noise bandwidth for the

horizontal system CTF and the vertical system CTF. The laboratory conditions can

be strictly controlled, which is important because in this calculation when Abar(fs) =

Aspc(fs), the MRTD will be undefined.

The laboratory MRTD in NVThermIP is difficult to compare directly to the

MRTD in FLIR92 for many reasons. Two of particular concern in this study were

the high, low, and user gain of NVThermIP - there is no equivalent in FLIR92 - and

the fact that NVThermIP calculates the MRTD for laboratory conditions which are

highly controlled and not equivalent to the conditions assumed in FLIR92. Since

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the laboratory MRTD outputted by NVThermIP is not directly comparable to the

MRTD from FLIR92, a work-around was proposed in conversations with Jon Hixson

(Army Research Labs, Fort Belvoir, VA). The CTF outputted from NVThermIP can

be manipulated to obtain an MRTD comparable to FLIR92 by multiplying 2 theSCT. NVThermIP produces a system CTF in the horizontal and vertical directions

following Equations 2.54a and 2.54b:

CT FHsys(fsh) =

[CT FHeye(fsh)]2 +

CT FHnoise(fsh)

SC Ntmp

2(2.54a)

CT FVsys(fsv) =

[CT FVeye(fsv)]2 +

CT FVnoise(fsv)

SC Ntmp

2(2.54b)

where the eye CTFs and the noise CTFs in the horizontal and vertical directions are

defined as

CT FHnoise(fsh) =

22detQHhor(fsh)QVhor

CT Feye

fsh

SMAG

MdispMT FHsys(fsh)

(2.56a)

CT FVnoise(fsv) =

22detQHverQVver(fsv)

CT Feye

fsv

SMAG

MdispMT FVsys(fsv)

(2.56b)

CT FHeye(fsh) =

CT Feye fsh

SMAG MdispMT FHsys(fsh) (2.56c)

CT FVeye(fsv) =CT Feye

fsv

SMAG

MdispMT FVsys(fsv)

. (2.56d)

The Mdisp is the display glare and is a proportionality constant of 169.6 Hz1

2 .

SC Ntmp is solicited from the user and considered a constant throughout calculations.

5. Detector Cooling in NVThermIP

NVThermIP allows for the selection of an uncooled detector. Selecting thisoption requires a user input of a performance measurement for the uncooled array

in terms of the measured detector noise, detector frame rate, f-number, and optics

transmission. Then, NVThermIP will calculate a peak D and integration time for

the uncooled sensor.

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6. Targeting Task Performance (TTP) Metric and NV-ThermIP

Unlike FLIR92 and previous version of of NVTherm, NVThermIP uses the

Targeting Task Performance (TTP) metric to predict the probability of successful

task performance. Since this study does not utilize the range performance predictions

from NVThermIP, no further details are provided here, but for more information, see

the NVThermIP Users Manual (NVESD 2005).

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III. OPTICAL TURBULENCE MODELCHOICE

Optical systems operating in a turbulent atmosphere experience broadening of

the point spread function, which is best described using a specific atmospheric MTF.

For a collimated beam passing through the atmosphere, turbulence distorts the shape

of the wavefront and causes variations of intensity along the wavefront so that when

the beam is brought back into focus by some optical system, the image formed has

been altered by the atmospheric affects. Driggers (1999) notes that the atmospheric

MTF may be expressed as two separate MTFs created by two different effects in the

atmosphere: scattering due to aerosols and blurring due to turbulence. In this study,

the MTF describing scattering due to aerosols is neglected.

This study uses the mathematical model of the atmospheric turbulence MTF

developed by Goodman (1985). Various mathematical determinations of the atmo-

spheric parameter C2n are considered for use in the atmospheric turbulence MTF

calculation, in order to most appropriately represent C2n through the whole atmo-

sphere.

A. OPTICAL TURBULENCE AND ATMOSPHERIC C2NAccording to the IREO Handbook Vol.2 (1993), turbulence in the atmosphere

creates random variations in the atmospheres index of refraction. These irregularities

distort the wavefronts that pass through them and thereby cause image distortion

or blur in imaging systems. Although there are different geometries for describing

turbulent systems, the applicable one in dealing with airborne and ground-based

sensors is spherical wave propagation. In this case, the propagating light comes from

sources that are in or near the turbulence, as in the imaging of objects in the turbulent

atmosphere. The sensors receiving the light are also in the turbulent atmosphere.

Although this study focuses on the airborne sensor situation where a target on the

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surface is imaged by an over-flying aircraft, it is important to note that it is the

turbulence at the sensor that most strongly affects the image quality.

Operationally, the best estimate of atmospheric turbulence would be deter-

mined from an analysis or forecast, but when a local estimate is not available, theatmospheric turbulence may be predicted using models that estimate the atmospheric

structure parameter C2n, as described below. The atmospheric structure parameter C2n

describes atmospheric variations in the index of refraction. Essentially, fluctuations

in the index of refraction along the path between the target and the sensor causes

some IR radiation to be randomly bent from the path, resulting in a blurred image

at the sensor. The more turbulent the atmosphere, the greater the blurring. C2n is

best defined by Equation 3.57,

C2n(x) = [n(x) n(x + r)]r2

3 (3.57)

where n(x) is the index of refraction at a point x in the atmosphere and n(x+r) is the

index of refraction some distance r away from x. The over-bar indicates an average

over the representative part of the atmosphere by either averaging n over time at one

location or space at a very short time (Goroch 1980).

Atmospheric variations in the index of refraction are described by C2n. The

generic form of how C2n varies in the atmosphere is given by Friehe (1977) as

C2n =

79 106 PT2

2 C2T + 0.113CTQ + 3.2 103C2Q

(3.58)

where P is the pressure in mb, T is the temperature in K, C2T is the temperature

structure function parameter, CTQ the temperature-water vapor parameter and CQ

the water vapor parameter, all in K2/m2

3 . The IREO Handbook Vol.2 (1993) states

that the dry-air, or C2T, term dominates in most applications since generally the C2TQ

and C2Q terms comprise no more than 2% of the total C2n. Since C

2T is typically the

dominant term in C2n, in this study it will be considered the only contributor. All

three structure parameters vary depending on location in the boundary layer (Fairall

1982). Although it will not be addressed in this study, it should be noted that in the

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microwave part of the spectrum, C2n depends much more strongly on the humidity

and CTQ and CQ are large contributors to the overall C2n (Fante 1980). Also, in

rare situations in the IR part of the spectrum, CTQ may be more significant (IREO

Handbook Vol.2 1993).

1. Turbulence Near the Ground

There are two primary ways that the ground impacts the movement of air and

causes turbulence. First, the free air stream flowing along the ground experiences

friction due to surface roughnesses, which causes wind shear. Second, the ground

may serve as a source or a sink for thermal energy of the air. Given sunny conditions

during the day, the ground will be a source of heat because the sun warms the ground

to a temperature higher than the air above it. This leads to thermal convection

and instability. At night, the ground will act as a heat sink by radiative cooling,

resulting in a ground temperature colder than the air above it. These conditions

are considered stable. When the air and the ground are at the same temperature,

atmospheric conditions are considered neutral. These extreme fluctuations in ground

temperature are observed over land, but over the ocean the temperature difference

between night and day is much less. The variation in temperature differences was the

primary motivation for comparing FLIR92 and NVThermIP over desert and marine

locations.

Fairall et. al. (1982) propose that in the surface layer of the atmosphere, the

structure function parameters have the forms of

C2T = T2

Z2

3 f() (3.59a)

C2Q = Q2

Z2

3 Af() (3.59b)

CTQ = rTQTQZ

2

3Af() (3.59c)

where T and Q are temperature and humidity scaling parameters in K and g/m3

respectively, f() is a dimensionless function, and rTQ is the temperature-humidity

correction parameter. Fairall et. al. (1982) gives an estimate value of 0.8 for rTQ in

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unstable conditions such as those being studied here. A is a constant, taken to be

0.6. Z is the height above the surface in m.

The dimensionless function f() is connected to the Richardson number, so it

accounts for varying conditions depending on the stability. Wyngaard et. al. (1971)determined the empirical form,

f() = 4.9(1 7.0) 23 < 0 (3.60a)f() = 4.9 = 0 (3.60b)

f() = 4.9(1 + 2.75) > 0 (3.60c)

where < 0 corresponds to unstable conditions (as under consideration here), = 0

is neutral and > 0 is stable. Wyngaard originally split f() into two segments of

0 and 0, but the neutral case has been added here to show when f() is aconstant. itself is defined as the height scaled by the Monin-Obukhov length scale,

=Z

L=

gZ

T + 0.61TaQ

Tau2

. (3.61)

L is the Monin-Obukhov length scale and is defined as the height over the ground

where the mechanically produced turbulence from vertical shear balances the dissi-

pative effect of negative buoyancy. In other words, the Richardson number equals

unity. L may be expressed as

L =Tau

2

g

T + 0.61TaQ

(3.62)where is the unitless von Karman constant that Fairall et. al. approximate to 0.35,

g is the gravitational acceleration on earth taken as 9.8 m/s2, Q is the humidity

scaling parameter in g/m3, is the density of air in kg/m3, and u is the frictional

velocity in m/s. In this case, the density of air is taken as 1.3 kg/m3. Ta is the

temperature of the ambient air in the region of interest, in K.

IfC2n is taken to primarily depend on C2T as was assumed above, then Equations

3.59b and 3.59c may be neglected and their terms in Equation 3.58 dropped. Davidson

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et. al. (1978) indicate that above the ocean and within 10m of the ocean surface,

C2T varies as Z

4

3 , but above that 10m, C2T varies as Z

2

3 . This is better seen by

solving Equation 3.59a for the conditions given in Equations 3.60, as shown below

where again =Z

L ,

C2T = 4.9T2

Z2

3 [1 7] 23 < 0 (3.63a)C2T = 4.9T

2

Z2

3 = 0 (3.63b)

C2T = 4.9T2

Z2

3 (1 + 2.75) > 0 (3.63c)

Substituting Equation 3.61into 3.63 for the three cases of unstable, neutral, and stable

C2T respectively, yields

C2T 4

3T2

Z4

3 L2

3 (3.64a)

C2T = 4.9T2

Z2

3 (3.64b)

C2T 13.5T2 Z1

3 L1. (3.64c)

In unstable conditions, || 1 (Equation 3.64a), so (1 7) 23 can be approximatedas (7) 23 . In the stable case, || 1 (Equation 3.64c), so (1 + 2.75) is approx-

imately 2.75. Other authors indicate that for || 1, C2T may even be taken as

independent of Z.

The above discussion applies over the ocean, but Hall (1977) observed that

in unstable conditions near land surface, C2n still decreases with height by Z

4

3 . The

Z4

3 height dependence frequently continues beyond 10m over land, but is still only

valid in the surface layer.

2. Turbulence Above the Surface Layer

In the so-called mixed layer above the surface layer, Fairall et. al. (1982) offer

definitions for C2T, C2Q, and CTQ where in all cases C

2n falls off as a function of Z

4

3 .

They are very similar to Equation 3.60, so in this study, Equation 3.60 is used beyond

the lowest surface layers.

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Above the mixed layer, one possible model of C2n behavior is the Hufnagel

model. Goodman (1985) offers a possible analytic approximation to how C2n varies in

the vertical and references the work by Hufnagel and Stanley (1964). This approxi-

mation isC2n(Z) = 2.7 1016

3 < u2 >

Z

10

10eZ + e

Z1.5

(3.65)

where Z is the location along the flight path in km and < u2 > is the mean value

of the squared wind speed. C2n is again in m

2

3 . This approximation reasonably rep-

resents the average variation of C2n in the middle to upper atmosphere but poorly

represents the boundary layer. Variations of C2n in the boundary layer differ exten-

sively depending on the stability of the boundary layer, as described above. Fante

(1980) and other sources indicate that the Hufnagel approximation agrees fairly well

with observation starting around 5 km above the surface.

3. Turbulence Through Whole Atmosphere

In this study, the atmospheric structure parameter C2n is taken to follow the

bulk method below 200 m and the Hufnagel formulation above the 5 km point. It is

worth noting that the Hufnagel formulation is an early numerical model of the upper

atmospheric structure parameter and is generally only considered valid for above 5km in the atmosphere. For simplicity in MatLab programming, between 200 m along

the pathlength and 5 km, an average value of 1 1016 m 23 was chosen. It is nearthe surface that C2n varies the most and is the largest, so the actual choice for C

2n

above the surface layer was of less concern than that in the surface layer. The C2n

calculation is summarized in Equation 3.66,

C2n = BulkMethod Z < 200m (3.66a)

C2n = 1 1016m2

3 200m < Z < 5000m (3.66b)

C2n = Huf nagelMethod Z > 5000m. (3.66c)

In order to test the validity of these assumptions, the bulk method and the Hufnagel

formulation were plotted for several temperature differences. In Figure 14, the surface

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temperature is taken to be 28C and the ambient air temperature 25C. Other param-

eters are given in Table IX, where for this test case, generic parameters are chosen.

The two methods intersect below 200 m, but at 200 m the C2n values are on the order

of 1 1016

m

2

3

, which agrees fairly well with results from Fairall et. al. (1982) andother sources. Values differed by less than an order of magnitude using the Hufnagel

model at 5 km. The choice of a constant C2n in the middle atmosphere simplified the

MatLab programming, but the small scale of C2n and the relatively small difference

between the two models around the 500 m to 5000 m layer suggested that choosing a

constant C2n was reasonably representative of the atmospheric conditions. Note that

for simplicity in the MatLab programming, the bulk method, which describes C2n in

the surface layer, is taken to be valid up to 200 m. This does not mean that the

surface layer itself extends up to 200 m. Rather, the bulk method is assumed valid

up to 200 m, so the bulk method may be assumed valid beyond the surface layer.

Table IX. Parameters for C2n Test Cases.Generic parameters chosen to test the Bulk and Hufnagel formulations of C2n.

Parameter Value Units

Rel Humidity Ambient Air 0.8 fractionRel Humidity Sfc Air 1.0 fractionWind Speed 7 m/sSfc Pressure 1012 hPaThermal Sfc Roughness 0.02 mMomentum Sfc Roughness 0.02 mTotal Pathlength 10,000 m

After comparing the bulk method and the Hufnagel method for a sample

test case, the two methods were compared for conditions at White Sands and Point

Conception (data give in Chapter IV). As indicated in Figures 15 and 16, the assumedconstant value of 11016 m 23 appears fairly representative between the two models.Also, the exponential behavior of the bulk method near the surface, in both cases,

indicates how much stronger turbulence is near the ground.

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Note that while the surface bulk model and Hufnagel model were used this

study, there are numerous other models of the atmospheric structure parameter. It

is also important to note that this study does not consider possible surface inversions

and neglects the stable case.

B. MTF FOR OPTICAL TURBULENCE

The Goodman (1985) formulation for atmospheric optical turbulence was cho-

sen for this study. It can be expressed for the long-exposure and short-exposure case,

although the focus here is on the long-exposure case.

The long-exposure and short-exposure atmospheric turbulence MTFs differ

10

18

10

17

10

16

10

15

10

14

10

130

50

100

150

200

250

300

350

400

Cn

2(m

2/3)

Height(m)

Comparing Cn

2Models Sfc T = 28

C, Amb T = 25

C

Sfc Bulk Model

Hufnagel Model

Bulk Method assumedvalid up to 200 m

Figure 14. Comparison of the Bulk and Hufnagel Methods with Sfc Temp 28C.At 28C, the two methods intersect at 158 m. At 200 m, the bulk method has a C2n

value of approximately 1 1016 m 23 . The bulk method is used below 200 m.

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substantially. In the long-exposure case, the exposure time is such that the phase and

log-amplitude vary over the course of the exposure. Thus during a long exposure, the

image recorded will be spread due to random variations in the tilt of the wavefront.

To consider the short-exposure case, a random factor associated with the wavefronttilt is extracted from the MTF before the average is taken. This is not done for the

long-exposure case. For the extremely short exposures, there will be no impact from

the wavefront tilt and it is ignored in determining the MTF (Fried 1966).

The derivation for the Goodman atmospheric MTF is summarized in Ap-

pendix A. Using the generic atmospheric input parameters given in Table IX, the

Goodman long exposure atmospheric turbulence MTF is orders of magnitude smaller

than the other MTFs included in FLIR92. In Figure 17, Goodman MTF is subtracted

1018

1016

1014

1012

0

1000

2000

3000

4000

5000

6000

7000

Cn

2(m

2/3)

Height(m)

Comparing Cn

2Models Sfc T = 75

C, Amb T = 35

C

Sfc Bulk Model

Hufnagel Model

Cn

2assumed constant

between 200m, 5000m

1 x 1016

m2/3

Figure 15. Comparison of the Bulk and Hufnagel Methods at White Sands.

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from unity to better illustrate the form of the MTF. The C2n used in the Goodman

calculations may be calculated using Equation 3.66.

From the above discussions, it appears that C2n is most significant near the

surface. In one illustration of this, the Goodman atmospheric MTF is examinedfor a variety of slant angles starting with a path perpendicular to the surface, and

ending with a virtually horizontal path through the surface layer, parallel to the

surface. Figure 18 illustrates the Goodman MTF at various slant angles, for a constant

pathlength of 100 m. Plotted is unity minus the Goodman MTF, as in Figure 17, to

best observe this small scale MTF. Although Figure 18 makes it clear that even close

to parallel to the surface, the Goodman MTF is small scale, still the resultant MTF

is more significant at smaller slant angles.

1018

1017

1016

1015

1014

1013

0

1000

2000

3000

4000

5000

6000

7000

Cn

2(m

2/3)

Height(m)

Comparing Cn

2Models Sfc T = 31

C, Amb T = 25

C

Sfc Bulk Model

Hufnagel Model

1 x 1016

m2/3

Cn

2assumed constant

between 200m, 5000m

Figure 16. Comparison of the Bulk and Hufnagel Methods at Pt Conception.

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0 5 10 151.4

1.2

1

0.8

0.6

0.4

0.2

0x 10

7 Goodman MTF 1

Spat Freq (cy/mrad)

MTF

Figure 17. Goodman Long Exposure Atmospheric Turbulence MTF.Note the small scale of the atmospheric turbulence MTF. Plot is of (1 - Goodman

MTF).

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0 5 10 154.5

4

3.5

3

2.5

2

1.5

1

0.5

0x 10

8

Spatial Frequency (cy/mrad)

MTF

Comparing (Goodman 1) MTF at Slant Angles

90 deg (perp sfc)

65 deg

35 deg

15 deg

1 deg (~horiz sfc)

Figure 18. Comparison of the Goodman MTF at Different Slant Angles.Perpendicular to the surface, the Goodman MTF is least significant and parallel to

the surface, most significant. In all cases, the Goodman MTF is small scale.

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IV. METHODS AND DATA SETS

A. SELECTION OF DATA LOCATIONS

This study compares MRTDs for marine and desert environments, with and

without an included MTF for atmospheric turbulence. Since this study is only an

initial comparison, only two sites were selected for analysis. Because of access to ac-

curate data, the White Sands Missile Range in New Mexico was selected for the desert

environment and Buoy 46063, just off Point Conception near Santa Barbara, CA was

selected for the marine environment. Although the two locations differ in nearly all

atmospheric conditions, the critical difference is between the surface temperature and

the ambient air temperature. As explained in Section III.A, the temperature struc-

ture parameter is the largest contributor to variations in the atmospheric structure

parameter.

B. SELECTION OF ATMOSPHERIC DATA

Atmospheric data for inclusion in TAWS and for calculation of parameters

in FLIR92 and NVThermIP were obtained from several sources. For the land lo-

cations, atmospheric data was obtained from the Weather Underground website,

www.wunderground.com. The website provided all the needed TAWS inputs. An

extreme example of the surface temperature and ambient air temperature at White

Sands was p

07Sep Hughes

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